BAM k is max

Algebra Level 3

Find the maximal value of kk , such that for all sets of positive real triples (a,b,c) (a, b, c) ,

a+b+c+3abc3k(ab+bc+ca). a+b+c + 3\sqrt[3]{abc} \geq k(\sqrt{ab} + \sqrt{bc} + \sqrt{ca}).

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